Yes, for about $30 you should get noticable improvement in all operations. Of course, for about $60 you'll get even more! I'm assuming you use DDR RAM and looking at prices of single 1GB modules.
If you post the make and model of your system board, we can verify exactly what RAM you should get. For example, if you do want to go to 2GBs, your MB may support a slightly faster RAM than you have now. (If you have, for example, DDR 333 / PC 2700 now and get DDR 400, a single added module will still run at the older 333 speed.)
Since you have an old system, be sure that any RAM you buy is returnable. Just in case it doesn't work.
Here's something that will give you some info about how your memory is being used now. Assuming you're running Win XP, press Ctrl-Alt-Del at one time, click on Performance. It'll show you some info. The Physical Memory shows in KB how your current RAM is being used. Divide by 1024 to get MBs - 1GB equals 1024 x 1024 x 1024. (The System Cache will increase when you add more RAM, so you can't expect all 512MBs to be given over to applications.)
Also note the Commit Charge - that Peak should show the max memory that's been called upon be a program since booting. Might check it after booting then again after running a game.
Also keep in mind that any money invested now in your system may be wasted if you are able to upgrade your components later - or sooner!